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Lesson Plans and Worksheets for Geometry

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More Lessons for Geometry

Common Core For Geometry

Student Outcomes

Students understand properties of area:

- Students understand that the area of a set in the plane is a number greater than or equal to zero that measures the size of the set and not the shape.
- The area of a rectangle is given by the formula length Γ width. The area of a triangle is given by the formula 1/2 base Γ height. A polygonal region is the union of finitely many non-overlapping triangular regions and has area the sum of the areas of the triangles.
- Congruent regions have the same area.
- The area of the union of two regions is the sum of the areas minus the area of the intersection.
- The area of the difference of two regions where one is contained in the other is the difference of the areas.

**Properties of Area**

Classwork

**Exploratory Challenge/Exercises 1β4**

- Two congruent triangles are shown below

a. Calculate the area of each triangle.

b. Circle the transformations that, if applied to the first triangle, would always result in a new triangle with the same area:

Translation Rotation Dilation Reflection

c. Explain your answer to part (b).

- a. Calculate the area of the shaded figure below.

b. Explain how you determined the area of the figure. - Two triangles β³ π΄π΅πΆ and β³ π·πΈπΉ are shown below. The two triangles overlap forming β³ π·πΊπΆ

a. The base of figure π΄π΅πΊπΈπΉ is composed of segments of the following lengths: π΄π· = 4, π·πΆ = 3, and πΆπΉ = 2. Calculate the area of the figure π΄π΅πΊπΈπΉ.

b. Explain how you determined the area of the figure. - A rectangle with dimensions 21.6 Γ 12 has a right triangle with a base 9.6 and a height of 7.2 cut out of the
rectangle.

a. Find the area of the shaded region.

b. Explain how you determined the area of the shaded region.

**Lesson Summary**

**SET (description)**: A set is a well-defined collection of objects called elements or members of the set.

**SUBSET**: A set π΄ is a subset of a set π΅ if every element of π΄ is also an element of π΅. The notation π΄ β π΅ indicates
that the set π΄ is a subset of set π΅.

**UNION**: The union of π΄ and π΅ is the set of all objects that are either elements of π΄ or of π΅, or of both. The union is
denoted π΄ βͺ π΅.

**INTERSECTION**: The intersection of π΄ and π΅ is the set of all objects that are elements of π΄ and also elements of π΅. The
intersection is denoted π΄ β© π΅.

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